Question

Describe the translation. y = (x - 6)^2 + 7 -- y = (x - 1)^2+ 3

Answer 1

We have the expression

$y=(x-6)^2+7$

and then we have:

$y=(x-1)^2+3$

If we want to go from the first expression to the second one we have to add 5 to the expression insde the square and substract 4 to the whole expression, that is:

$\begin{gathered} y=(x-6+5)^2+7-4 \\ y=(x-1)^2+3 \end{gathered}$

Since we add 5 units to the variable x, this means that we translate the graph 5 units to the left. Furthermore, since we substract 4 units to the whole expression this means that we translate the graph four units down.

Therefore, the translation moves the graph 5 units to the left and 4 units down the original graph